Hello Amanda, your koma is not wrong. I am a nagauta player too and your koma, as you have explained it, sounds just right.
As nagauta and tsugaru shamisens play different styles, they are set up purposefully differently. Although this doesn’t stop nagauta pieces being played on a tsugaru (and vice versa), the tunes for each style of shamisen were written specifically to take into account the set up of each kind of shamisen. Your koma should be high and ichi and san no ito right at the edges of the sao.
The main reason the koma is high for nagauta shamisens is to stop the strings making too much of a ‘rasping’ sound when played. On tsugaru shamisens there is a screw at the back of the neck which allows the player to raise the string to ajust the level of ‘rasp’. So the koma can be lower and yet a cleaner sound can still be achieved. However, because nagauta shamisens don’t have this facility, the koma is purposefully made higher, to cut out too much ‘rasping’. I have tried using a tsugaru koma on my nagauta shamisen, but always end up having to raise the strings by putting a cocktail stick under the strings at the ito maki end. So I don’t recommend changing your koma.
As for touching the strings when playing san no ito, this too is normal, (because of the higher koma). There are two stylistic options and it depends on the speed of the piece you are playing, as to which is most practical. You can just rotate your hand round a little further, (when playing the top string), to give you more of an arch in the gap under your fingers. However, my teacher told me that I should just lift my finger off, after playing the top string, so that the other strings are clear, (even if this meant rapidly lifting and lowering several times in a row during playing).
I hope this helps, if any of it doesn’t make sense let me know and I’ll try and help further. Good luck!